It's not too late, even though I do think your chances are best if you apply early and you might want to check the application deadlines for the programs you're considering adding since I think some programs have an earlier deadline than others.
I ended up applying to a certain program in late Nov/early Dec (the reason I was so late in applying to it was because I had heard something about the program at another interview that made me decide I wanted to check it out). They sent me an interview invitation within a week. 🙂 I definitely wouldn't recommend applying that late if you can avoid it, but if you're truly worried you might not get enough interviews then it's better to try sending more applications than it is to risk ending up in SOAP.
That being said, an AMG should be able to match with 40 applications - are you concerned about a red flag on your application?